1. Related Applications
The subject matter of the present application is related to U.S. patent application Ser. No. 07/901,044 filed Jun. 22, 1992 entitled Automatic Cross-Directional Controls Zone Alignment for Sheetmaking Systems now U.S. Pat. No. 5,400,258 and U.S. patent application Ser. No. 08/115,598 filed on even date herewith entitled Self-System Parameter Identification for Systems with Pure Time-Delay, both incorporated herein by reference.
2. Field of the Invention
The present invention relates to system identification of a cross-directional control system of a type used, for example, in sheetmaking process. In particular, the invention relates to techniques for increasing the signal-to-noise ratio of measurements used in identification of such systems.
3. State of the Art
In sheetmaking processes, on-line quality measurements and controls are used to control the quality of the product. In modem automated papermaking machines, for example, continuous paper webs, sometimes measuring as much as 400 inches across, can be produced at rate of up to 100 feet per second. To control the quality of the paper manufactured at such rates and to reduce the quantity of finished product that must be rejected if there are upsets in the manufacturing processes, properties of the paper web must be measured and adjusted while the machines are operating.
Referring to FIGS. 1 and 2, in a papermaking process, a slurry of paper fibers and water mixture (or stock) is fed into a tank 10 called a "headbox", and the slurry then flows continuously through an opening 35 defined by a "slice lip" 34. The slurry is deposited onto a continuous conveyor belt, or "wire" 13. The wire moves in a direction away from the headbox. The slurry thus forms a continuous mat 18 on the wire. The mat of paper slurry drains some of its water content as it is being transported by the wire and becomes a sheet that is then pressed by rollers 21 to remove additional moisture from the sheet. The "basis weight" (mass per unit area) or other property of the sheet is then measured using a sensor, typically a scanning sensor 30 as shown in FIG. 1.
The vertical position of the slice lip is related to the size of the feed opening and hence to the amount of slurry deposited on the wire and ultimately to the basis weight of the sheet. The vertical position of the slice lip is controlled by a plurality of actuators 23 connected to the slice lip and to the headbox. Using information from a sensor, the actuators may be controlled to obtain the desired basis weight of the sheet.
Machines which produce webs of sheet material such as paper, plastic and aluminum, face process control problems in producing webs which satisfy specifications for the given sheet material. Web specifications commonly include ranges for characteristics of the web including thickness, moisture content, weight per unit area, and the like. Quality control is complicated since the specified characteristics vary in both the machine direction (MD), or direction of movement of the web through the machine, and in the machine cross direction (CD), or laterally across the web.
The MD variations are generally affected by factors that impact the entire width of the web, such as machine speed, the source of base material being formed into a web by the machine, supplies of working media like steam, and similar factors. CD variations, represented by profiles or profound signals, are normally controlled by arrays of actuation cells distributed across the width of the machine. On paper making machines, the CD actuation cells include basis weight actuators which control the slice of a headbox, steam shower nozzles, infrared heaters which control CD moisture variations, and other known devices.
To maintain the CD quality profile of the sheet with CD actuators, it is important in know the effect of each actuator unit's adjustment. This effect has two aspects, namely spatial effect and time effect. The spatial effect is normally characterized by mapping and spatial response. Mapping describes the alignment of each actuator unit to its affected portion of measured profile. Spatial response describes the pattern of the profile change due to each actuator adjustment. The time effect refers to the relation between the adjustments of an actuator and the changes of its corresponding portion of the profile in terms of their dynamic evolution over time. It is characterized as dynamic response. This invention relates to a method of identifying the dynamic response of CD control actuators.
As described in U.S. patent application Ser. No. 07/901,044, an automated tool may be used for identifying mapping and spatial response through a bump test. The same bump test result may be used to identify dynamic response of the CD control actuators. The dynamic response may be parameterizod as a time delay, a time constant, and a process gain.
A typical response to a bump excitation is shown in FIG. 3. If the bump is applied at time t.sub.0, then some time later at time t.sub.1 the measured sheet property will begin to change at some rate and will continue to change at a rate that gradually decreases until the system reaches a steady state condition. The amount of change of the sheet property, i.e., the amplitude of the response, A.sub.R, divided by the amplitude of the bump excitation, A.sub.B, is defined as the process gain. The time t.sub.1 -t.sub.0 is defined as the delay of the system, T.sub.D ; and the time at which the system would reach steady state if the measured sheet property changed at a non-decreasing rate is defined as the time constant of the system, T.sub.C. For a time-invariant, first-order linear system, the foregoing parameters completely describe the system's behavior.
Thus, given a step response of a linear system, system parameters can be identified, for example, using a Least-Square (LS) algorithm, with little difficulty. However, noise in the response measurement, over a short transient response can be fatal to the identification result. Hence, multiple step disturbances, rather than one or two, and thus a longer response measurement time, may be required to obtain an acceptable identification result.
The foregoing situation is illustrated in FIG. 4. A long sequence of disturbances x(t) is applied to a plant. The plant may be, for example, a sheetmaking system subject to considerable process noise. The output of the plant is measured, producing a long sequence of noisy measurements y(t). The disturbances x(t) are also input to a model identification processor, which estimates the plant output. The estimated plant output is compared to the measured plant output y(b) to produce an error signal e(t), which is used to adjust the model. As the signal-to-noise ratio of the measurements decreases the length of time required for successful system identification generally increases.
In determining mapping and spatial response, cross-directional information is vitally important. In determining system parameters, on the other hand, such as time delay, time constant and process gain, cross-directional measurements through a transient response time include redundant information. Since all the actuators of the cross-direction are substantially identical and have substantially identical characteristics, each actuator is assumed to exhibit substantially the same time delay, time constant and gain.
The present invention takes advantage of the redundancy of redundant noisy measurements to produce a synthetic measurement having a higher signal-to-noise ratio that may be used to perform system identification a relatively shorter period of time, within one or two step response times.